Schools Chancellor Rudy Crew — denied an extension on his $245,000-a- year contract by the Board of Education — said yesterday he won’t be back at work after the holidays.

“The system needs continuity, but I don’t think it makes sense for me to remain, given the nature of what happened,” Crew said yesterday of the six months left on his contract.

“It would be ridiculous to say, ‘Hey let’s have a board meeting,’ or ‘Let’s go on a retreat,” said Crew outside his city-owned home in Brooklyn Heights.

Despite the nasty battle over his future, Crew said he has “no regrets” about his 31/2-year run as head of the nation’s largest school system.

“I don’t have reason to be angry. I had a good, long run here. I have no regrets at all. I’d do it all over again, even knowing what I know.”

Board members on both sides of Thursday’s close contract vote say that a buyout would be best — for both Crew and the school system.

“My gut feeling is he probably won’t return after the holiday,” said Staten Island board member Jerry Camaratta, who was among those voting to deny Crew a new contract.

Camaratta predicted the board would put a buyout on the front-burner, beginning at its meeting Tuesday morning.

Board President Bill Thompson, one of Crew’s staunchest backers, said in the aftermath of Thursday’s vote that it would be “unfair” to ask him to continue for six months without the board’s full support.

Mayor Giuliani yesterday ducked questions on whether Crew should pack up right away, saying it’s between the board and the chancellor.

“If he leaves, we’ll proceed quickly to find an interim,” said Giuliani.

But the mayor wasn’t shedding any tears over an early departure by Crew, once among his closest allies before the two had a falling out over the mayor’s proposal to fund private-school vouchers.

“What we should be looking for, either on an interim or long-term basis, is a leader who can thoroughly reform the system and make it work for the children rather than maintain it as a job-protection system,” said Giuliani.

While Giuliani tried to distance himself from any direct role in the board vote, Crew laid the blame for his demise squarely on the shoulders of a mayor readying for a Senate run against first lady Hillary Clinton.

“What happened was the mayor and his supporters did what they wanted to do,” said Crew. “I always thought something like this would happen with the election only a few months down the road.”

Clinton spokesman Howard Wolfson said Crew’s “ouster raises very serious questions” about Giuliani’s legislative skills. “The mayor’s instinct when he disagrees with someone is to either fire them, sue them or arrest them. That won’t work in the U.S. Senate.”

Giuliani fired back: “I say Merry Christmas to everyone, including some press flack who can’t figure out how to celebrate Christmas.”